First question: In the book they fight for a long time at the bottom with the Balrog's flame quenched and then they climb the endless stair which the dwarves built and reach the top of the mountain, where the balrog's flame is reignited. Gandalf throws the balrog down, destroying the mountainside in the process, but he himself also dies. However he is sent back in a more powerful form to complete his mission (the mission of the Istari (wizards) was to rid Middle Earth of Sauron).
Second question: magic isn't as visible in the world of LotR as in D&D. Spells are rarely seen, they are more like long lasting enchantments and creation of magical objects.
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